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طريقة تنصيف الفترات Bisection Method

This technique based on the Intermediate Value Theorem Suppose f is a continuous function defined on the interva [a; b], with f(a) and f(b) of opposite sign. The Intermediate Value Theorem implies that a number p exists in (a; b) with f(p) = 0. The method calls for a repeated halving of subintervals of [a; b] and, at each step, locating  the half containing p. To begin, set a1 = a and b1 = b, and let p1 be the midpoint of [a; b]; that is,

p1=a1+b1-a1/2=a1+b1/2

 If f(p1) = 0, then p = p1, and we are done

 If f(p1) is not equal 0, then f(p1) has the same sign as either f(a1) or f(b1)

 If f(p1) and f(a1) have the same sign, p belond (p1; b1). Set a2 = p1 and b2 = b1

If f(p1) and f(a1) have opposite signs, p belond (a1; p1). Set a2 = a1 and b2 = p1

لمتابعة المحاضرة على اليوتيوب

طريقة تنصيف الفترات Bisection Method

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